Subgroups — #4009

Order 160.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
3	D₅⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×AGL(1,𝔽₅)	—	2	1	no	—
5	C₅×Q₈	C₄	1	1	yes	characteristic, complemented
6	C₄×D₅	—	2	1	no	—
7	C₄×D₅	C₂²	1	1	yes	characteristic
8	Dic₁₀	—	2	1	no	—
9	Dic₁₀	C₄	1	1	yes	characteristic, complemented
10	#170	—	2	1	no	—
11	#103	—	5	1	no	maximal, Sylow
12	C₂×D₅	D₄	1	1	yes	characteristic
13	AGL(1,𝔽₅)	—	4	1	no	—
14	C₄×C₅	—	2	1	no	—
15	C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	Dic₅	—	2	1	no	—
17	Dic₅	D₄	1	1	yes	characteristic
18	C₂×Q₈	—	5	1	no	—
19	C₂×C₈	—	5	1	no	—
20	C₄⋊C₄	—	5	1	no	—
21	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
22	D₅	SD₁₆	1	1	yes	characteristic
23	D₅	Q₁₆	1	1	yes	characteristic
24	Q₈	—	5	1	no	—
25	Q₈	—	10	1	no	—
26	Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
27	C₂×C₄	—	5	1	no	—
28	C₂×C₄	—	10	1	no	—
29	C₂×C₄	—	10	1	no	—
30	C₈	—	10	1	no	—
31	C₅	#103	1	1	yes	characteristic, complemented, Sylow
32	C₂²	—	5	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	5	1	no	—
35	C₄	—	10	1	no	—
36	C₄	—	20	1	no	—
37	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
38	C₂	—	5	1	no	—
39	C₂	—	5	1	no	—
40	C₂	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.